{"paper":{"title":"A construction of two different solutions to an elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Jacek Cyranka, Piotr Bogus{\\l}aw Mucha","submitted_at":"2015-02-11T16:29:37Z","abstract_excerpt":"The paper aims at constructing two different solutions to an elliptic system\n  $$ u \\cdot \\nabla u + (-\\Delta)^m u = \\lambda F\n  $$ defined on the two dimensional torus.\n  It can be viewed as an elliptic regularization of the stationary Burgers 2D system.\n  A motivation to consider the above system comes from an examination of unusual propetries of the linear operator\n  $\\lambda \\sin y \\partial_x w + (-\\Delta)^{m} w$ arising from a linearization of the equation about the dominant part of $F$.\n  We argue that the skew-symmetric part of the operator provides in some sense a smallness of norms of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03363","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}